Field and Galois theory resources

Notes and review

• UCSD field theory qual review.

• Calculating a Galois group from a polynomial – review notes on discriminants of cubics, splitting fields of polynomials of prime degree, cyclotomic extensions, and the Frobenius automorphism of finite fields, with worked computations over \(\QQ\) and over finite fields.

• Galois theory notes (Edinburgh)

• Conrad, Some examples of the Galois correspondence

Problems

• Tate, Galois theory problems

• Galois-group practice problems

• MIT fields and Galois theory: problems for discussion, combined problem file, and hints and solutions.

• Additional MIT qual problems: Spring 2016 A5, Fall 2016 M2, Fall 2012 M5, Fall 2014 A5, Spring 2012 A9, Fall 2013 A4, Spring 2016 M5.